A method for the enumeration of various classes of column-convex polygons

We present a new method that allows to enumerate many classes of column-convex polygons, according to their perimeter, width and area. The first step of this method leads to a functional equation which defines implicitly the generating function for the class of polygons under consideration. The second step consists in solving this equation. We apply systematically our method to all the usual classes of column-convex polygons: thus, we first refine some already known results for parallelogram polygons, directed and convex polygons, and convex polygons, and then vie obtain two new results, namely the generating function for column-convex polygons and directed column-convex polygons.